機器學習sklearn19.0聚類演算法——Kmeans演算法
阿新 • • 發佈：2019-01-08
一、關於聚類及相似度、距離的知識點
二、k-means演算法思想與流程
三、sklearn中對於kmeans演算法的引數
四、程式碼示例以及應用的知識點簡介
（1）make_blobs：聚類資料生成器
sklearn.datasets.make_blobs(n_samples=100, n_features=2,centers=3, cluster_std=1.0, center_box=(-10.0, 10.0), shuffle=True, random_state=None)[source]
返回值為：
（2）np.vstack方法作用——堆疊陣列
詳細介紹參照部落格連結：http://blog.csdn.net/csdn15698845876/article/details/73380803
#!/usr/bin/env python # -*- coding:utf-8 -*- # Author:ZhengzhengLiu #k-means聚類演算法 import numpy as np import pandas as pd import matplotlib as mpl import matplotlib.pyplot as plt import matplotlib.colors import sklearn.datasets as ds from sklearn.cluster import KMeans #引入kmeans #解決中文顯示問題 mpl.rcParams['font.sans-serif'] = [u'SimHei'] mpl.rcParams['axes.unicode_minus'] = False #產生模擬資料 N = 1500 centers = 4 #make_blobs:聚類資料生成器 data,y = ds.make_blobs(N,n_features=2,centers=centers,random_state=28) data2,y2 = ds.make_blobs(N,n_features=2,centers=centers,random_state=28) data3 = np.vstack((data[y==0][:200],data[y==1][:100],data[y==2][:10],data[y==3][:50])) y3 = np.array([0]*200+[1]*100+[2]*10+[3]*50) #模型的構建 km = KMeans(n_clusters=centers,random_state=28) km.fit(data,y) y_hat = km.predict(data) print("所有樣本距離聚簇中心點的總距離和:",km.inertia_) print("距離聚簇中心點的平均距離:",(km.inertia_/N)) print("聚簇中心點:",km.cluster_centers_) y_hat2 = km.fit_predict(data2) y_hat3 = km.fit_predict(data3) def expandBorder(a, b): d = (b - a) * 0.1 return a-d, b+d #畫圖 cm = mpl.colors.ListedColormap(list("rgbmyc")) plt.figure(figsize=(15,9),facecolor="w") plt.subplot(241) plt.scatter(data[:,0],data[:,1],c=y,s=30,cmap=cm,edgecolors="none") x1_min,x2_min = np.min(data,axis=0) x1_max,x2_max = np.max(data,axis=0) x1_min,x1_max = expandBorder(x1_min,x1_max) x2_min,x2_max = expandBorder(x2_min,x2_max) plt.xlim((x1_min,x1_max)) plt.ylim((x2_min,x2_max)) plt.title("原始資料") plt.grid(True) plt.subplot(242) plt.scatter(data[:, 0], data[:, 1], c=y_hat, s=30, cmap=cm, edgecolors='none') plt.xlim((x1_min, x1_max)) plt.ylim((x2_min, x2_max)) plt.title(u'K-Means演算法聚類結果') plt.grid(True) m = np.array(((1, 1), (0.5, 5))) data_r = data.dot(m) y_r_hat = km.fit_predict(data_r) plt.subplot(243) plt.scatter(data_r[:, 0], data_r[:, 1], c=y, s=30, cmap=cm, edgecolors='none') x1_min, x2_min = np.min(data_r, axis=0) x1_max, x2_max = np.max(data_r, axis=0) x1_min, x1_max = expandBorder(x1_min, x1_max) x2_min, x2_max = expandBorder(x2_min, x2_max) plt.xlim((x1_min, x1_max)) plt.ylim((x2_min, x2_max)) plt.title(u'資料旋轉後原始資料圖') plt.grid(True) plt.subplot(244) plt.scatter(data_r[:, 0], data_r[:, 1], c=y_r_hat, s=30, cmap=cm, edgecolors='none') plt.xlim((x1_min, x1_max)) plt.ylim((x2_min, x2_max)) plt.title(u'資料旋轉後預測圖') plt.grid(True) plt.subplot(245) plt.scatter(data2[:, 0], data2[:, 1], c=y2, s=30, cmap=cm, edgecolors='none') x1_min, x2_min = np.min(data2, axis=0) x1_max, x2_max = np.max(data2, axis=0) x1_min, x1_max = expandBorder(x1_min, x1_max) x2_min, x2_max = expandBorder(x2_min, x2_max) plt.xlim((x1_min, x1_max)) plt.ylim((x2_min, x2_max)) plt.title(u'不同方差的原始資料') plt.grid(True) plt.subplot(246) plt.scatter(data2[:, 0], data2[:, 1], c=y_hat2, s=30, cmap=cm, edgecolors='none') plt.xlim((x1_min, x1_max)) plt.ylim((x2_min, x2_max)) plt.title(u'不同方差簇資料的K-Means演算法聚類結果') plt.grid(True) plt.subplot(247) plt.scatter(data3[:, 0], data3[:, 1], c=y3, s=30, cmap=cm, edgecolors='none') x1_min, x2_min = np.min(data3, axis=0) x1_max, x2_max = np.max(data3, axis=0) x1_min, x1_max = expandBorder(x1_min, x1_max) x2_min, x2_max = expandBorder(x2_min, x2_max) plt.xlim((x1_min, x1_max)) plt.ylim((x2_min, x2_max)) plt.title(u'不同簇樣本數量原始資料圖') plt.grid(True) plt.subplot(248) plt.scatter(data3[:, 0], data3[:, 1], c=y_hat3, s=30, cmap=cm, edgecolors='none') plt.xlim((x1_min, x1_max)) plt.ylim((x2_min, x2_max)) plt.title(u'不同簇樣本數量的K-Means演算法聚類結果') plt.grid(True) plt.tight_layout(2, rect=(0, 0, 1, 0.97)) plt.suptitle(u'資料分佈對KMeans聚類的影響', fontsize=18) plt.savefig("k-means聚類演算法.png") plt.show() #執行結果： 所有樣本距離聚簇中心點的總距離和: 2592.9990199 距離聚簇中心點的平均距離: 1.72866601327 聚簇中心點: [[ -7.44342199e+00 -2.00152176e+00] [ 5.80338598e+00 2.75272962e-03] [ -6.36176159e+00 6.94997331e+00] [ 4.34372837e+00 1.33977807e+00]]
程式碼中用到的知識點：
#!/usr/bin/env python # -*- coding:utf-8 -*- # Author:ZhengzhengLiu #kmean與mini batch kmeans 演算法的比較 import time import numpy as np import matplotlib as mpl import matplotlib.pyplot as plt import matplotlib.colors from sklearn.cluster import KMeans,MiniBatchKMeans from sklearn.datasets.samples_generator import make_blobs from sklearn.metrics.pairwise import pairwise_distances_argmin #解決中文顯示問題 mpl.rcParams['font.sans-serif'] = [u'SimHei'] mpl.rcParams['axes.unicode_minus'] = False #初始化三個中心 centers = [[1,1],[-1,-1],[1,-1]] clusters = len(centers) #聚類數目為3 #產生3000組二維資料樣本，三個中心點，標準差是0.7 X,Y = make_blobs(n_samples=300,centers=centers,cluster_std=0.7,random_state=28) #構建kmeans演算法 k_means = KMeans(init="k-means++",n_clusters=clusters,random_state=28) t0 = time.time() k_means.fit(X) #模型訓練 km_batch = time.time()-t0 #使用kmeans訓練資料消耗的時間 print("K-Means演算法模型訓練消耗時間:%.4fs"%km_batch) #構建mini batch kmeans演算法 batch_size = 100 #取樣集的大小 mbk = MiniBatchKMeans(init="k-means++",n_clusters=clusters,batch_size=batch_size,random_state=28) t0 = time.time() mbk.fit(X) mbk_batch = time.time()-t0 print("Mini Batch K-Means演算法模型訓練消耗時間:%.4fs"%mbk_batch) #預測結果 km_y_hat = k_means.predict(X) mbk_y_hat = mbk.predict(X) #獲取聚類中心點並對其排序 k_means_cluster_center = k_means.cluster_centers_ mbk_cluster_center = mbk.cluster_centers_ print("K-Means演算法聚類中心點:\n center=",k_means_cluster_center) print("Mini Batch K-Means演算法聚類中心點:\n center=",mbk_cluster_center) order = pairwise_distances_argmin(k_means_cluster_center,mbk_cluster_center) #畫圖 plt.figure(figsize=(12,6),facecolor="w") plt.subplots_adjust(left=0.05,right=0.95,bottom=0.05,top=0.9) cm = mpl.colors.ListedColormap(['#FFC2CC', '#C2FFCC', '#CCC2FF']) cm2 = mpl.colors.ListedColormap(['#FF0000', '#00FF00', '#0000FF']) #子圖1——原始資料 plt.subplot(221) plt.scatter(X[:,0],X[:,1],c=Y,s=6,cmap=cm,edgecolors="none") plt.title(u"原始資料分佈圖") plt.xticks(()) plt.yticks(()) plt.grid(True) #子圖2：K-Means演算法聚類結果圖 plt.subplot(222) plt.scatter(X[:,0], X[:,1], c=km_y_hat, s=6, cmap=cm,edgecolors='none') plt.scatter(k_means_cluster_center[:,0], k_means_cluster_center[:,1],c=range(clusters),s=60,cmap=cm2,edgecolors='none') plt.title(u'K-Means演算法聚類結果圖') plt.xticks(()) plt.yticks(()) plt.text(-3.8, 3, 'train time: %.2fms' % (km_batch*1000)) plt.grid(True) #子圖三Mini Batch K-Means演算法聚類結果圖 plt.subplot(223) plt.scatter(X[:,0], X[:,1], c=mbk_y_hat, s=6, cmap=cm,edgecolors='none') plt.scatter(mbk_cluster_center[:,0], mbk_cluster_center[:,1],c=range(clusters),s=60,cmap=cm2,edgecolors='none') plt.title(u'Mini Batch K-Means演算法聚類結果圖') plt.xticks(()) plt.yticks(()) plt.text(-3.8, 3, 'train time: %.2fms' % (mbk_batch*1000)) plt.grid(True) plt.savefig("kmean與mini batch kmeans 演算法的比較.png") plt.show() #執行結果： K-Means演算法模型訓練消耗時間:0.2260s Mini Batch K-Means演算法模型訓練消耗時間:0.0230s K-Means演算法聚類中心點: center= [[ 0.96091862 1.13741775] [ 1.1979318 -1.02783007] [-0.98673669 -1.09398768]] Mini Batch K-Means演算法聚類中心點: center= [[ 1.34304199 -1.01641075] [ 0.83760683 1.01229021] [-0.92702179 -1.08205992]]
五、聚類演算法的衡量指標
#!/usr/bin/env python
# -*- coding:utf-8 -*-
# Author:ZhengzhengLiu
#聚類演算法評估
import time
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import matplotlib.colors
from sklearn.cluster import KMeans,MiniBatchKMeans
from sklearn import metrics
from sklearn.metrics.pairwise import pairwise_distances_argmin
from sklearn.datasets.samples_generator import make_blobs
#解決中文顯示問題
mpl.rcParams['font.sans-serif'] = [u'SimHei']
mpl.rcParams['axes.unicode_minus'] = False
#初始化三個中心
centers = [[1,1],[-1,-1],[1,-1]]
clusters = len(centers) #聚類數目為3
#產生3000組二維資料樣本，三個中心點，標準差是0.7
X,Y = make_blobs(n_samples=300,centers=centers,cluster_std=0.7,random_state=28)
#構建kmeans演算法
k_means = KMeans(init="k-means++",n_clusters=clusters,random_state=28)
t0 = time.time()
k_means.fit(X) #模型訓練
km_batch = time.time()-t0 #使用kmeans訓練資料消耗的時間
print("K-Means演算法模型訓練消耗時間:%.4fs"%km_batch)
#構建mini batch kmeans演算法
batch_size = 100 #取樣集的大小
mbk = MiniBatchKMeans(init="k-means++",n_clusters=clusters,batch_size=batch_size,random_state=28)
t0 = time.time()
mbk.fit(X)
mbk_batch = time.time()-t0
print("Mini Batch K-Means演算法模型訓練消耗時間:%.4fs"%mbk_batch)
km_y_hat = k_means.labels_
mbkm_y_hat = mbk.labels_
k_means_cluster_centers = k_means.cluster_centers_
mbk_means_cluster_centers = mbk.cluster_centers_
print ("K-Means演算法聚類中心點:\ncenter=", k_means_cluster_centers)
print ("Mini Batch K-Means演算法聚類中心點:\ncenter=", mbk_means_cluster_centers)
order = pairwise_distances_argmin(k_means_cluster_centers,
mbk_means_cluster_centers)
#效果評估
### 效果評估
score_funcs = [
metrics.adjusted_rand_score, #ARI（調整蘭德指數）
metrics.v_measure_score, #均一性與完整性的加權平均
metrics.adjusted_mutual_info_score, #AMI（調整互資訊）
metrics.mutual_info_score, #互資訊
]
## 2. 迭代對每個評估函式進行評估操作
for score_func in score_funcs:
t0 = time.time()
km_scores = score_func(Y, km_y_hat)
print("K-Means演算法:%s評估函式計算結果值:%.5f；計算消耗時間:%0.3fs" % (score_func.__name__, km_scores, time.time() - t0))
t0 = time.time()
mbkm_scores = score_func(Y, mbkm_y_hat)
print("Mini Batch K-Means演算法:%s評估函式計算結果值:%.5f；計算消耗時間:%0.3fs\n" % (score_func.__name__, mbkm_scores, time.time() - t0))
#執行結果：
K-Means演算法模型訓練消耗時間:0.6350s
Mini Batch K-Means演算法模型訓練消耗時間:0.0900s
K-Means演算法聚類中心點:
center= [[ 0.96091862 1.13741775]
[ 1.1979318 -1.02783007]
[-0.98673669 -1.09398768]]
Mini Batch K-Means演算法聚類中心點:
center= [[ 1.34304199 -1.01641075]
[ 0.83760683 1.01229021]
[-0.92702179 -1.08205992]]
K-Means演算法:adjusted_rand_score評估函式計算結果值:0.72566；計算消耗時間:0.071s
Mini Batch K-Means演算法:adjusted_rand_score評估函式計算結果值:0.69544；計算消耗時間:0.001s
K-Means演算法:v_measure_score評估函式計算結果值:0.67529；計算消耗時間:0.004s
Mini Batch K-Means演算法:v_measure_score評估函式計算結果值:0.65055；計算消耗時間:0.004s
K-Means演算法:adjusted_mutual_info_score評估函式計算結果值:0.67263；計算消耗時間:0.006s
Mini Batch K-Means演算法:adjusted_mutual_info_score評估函式計算結果值:0.64731；計算消耗時間:0.005s
K-Means演算法:mutual_info_score評估函式計算結果值:0.74116；計算消耗時間:0.002s
Mini Batch K-Means演算法:mutual_info_score評估函式計算結果值:0.71351；計算消耗時間:0.001s